Page 54 - SM inner class 7.cdr

(b) (ii) 0000086. = 86 = 86 = 86
´
.38 38 ´ 10 - 1 1000000 10 6 10 10 5
.
.
.038 38 ´ 10 - 2 = 86 ´10 -5 = 86 10 -5
.
´
.0038 38 ´ 10 - 3 10
.
.
.00038 38 ´ 10 - 4 Ex am ple 10. Write the fol low ing num bers in
.000038 38 ´ 10 - 5 stan dard form
.
.
.0000038 38 ´ 10 - 6
(i) Twenty six lakh (ii) 725649
We can say the following. (iii) 0.000772 (iv) 42012.5
(i) To express any number in scientific So lu tion :
notation, only one digit (other than 0) is to (i) Twenty six lakh = 26 00 000, ,
be kept on the left side of the decimal. 6
=
= 2.600000 ´1000000 2.6 ´ 10
(ii) In the scientific notation of a number less (ii) 725646 = 7 25646 100000
´
.
than 1, the index of 10 is a negative 5
´
.
= 725646 10
integer and this integer is equal to the 772 772
.
.
number of places the decimal moves to (iii) 0000772. = 10000 = 5
the right. 10
(iv) 42012.5 = 4.20125 10000
´
(iii) In the scientific notation of the number
greater than 1, the index of 10 is a = 4.20125 ´10 4
positive integer and this index is equal to
Ex am ple 11. Write each of the following
the number of places the decimal moves
to the left. num bers in the usual (i e. . nor mal) form
(i) 125 10. ´ 8 (ii) 22 10. ´ - 12
Ex am ple 9. Ex press the fol low ing num bers in
125 125
8
sci en tific no ta tion : So lu tion : (i) 125 10. ´ 8 = ´ 10 = ´ 10 8
100 10 2
(i) 0.52 (ii) 0.000086
´
52 52 1 1 =125 10 8 - 2
.
So lu tion : (i) 052. = = ´ = 52 ´
100 10 10 10 1 =125 10 6
´
.
= 52 10 -1 =12500000
´
E xercise 5.4
1. Ex press the fol low ing as sin gle ex po nents.
)
(a) ( )2 3 5 (b) (10 2 2 (c) (-3 4 5 (d) ( )p 2 3
)
3 6
é æ - ö 1 3 ù é 2 æ ö 3 ù
(e) (-m 4 4 (f) (x a b (g) ç ê ÷ ú (h) ç ÷ ú
)
)
ê
ê è 3 ø ú ê 9 è ø ú û
ë
ë
û
n
é æ pö m ù
(i) ê ç ÷ ú
ê è qø ú û
ë
2. Change the fol low ing neg a tive ex po nents into pos i tive ex po nents.
- 4
2 æ ö
(a) ( )12 - 3 (b) ( )-a -2 (c) (100 ) - 5 (d) ç ÷
3 è ø
-9 - b
æ - ö 1 x æ ö
(e) ç ÷ (f) ç ÷
è 10 ø y è ø
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Mathematics In Focus - 7